Nowadays, artificial intelligence (AI) and deep learning (DL) progressively adapt to various spheres of our lives. These disciplines contain safety-critical applications such as autonomous driving with a high risk of human injury in the case of malfunction, requiring a high promise of dependability. Even the dependability becomes more crucial as shrinking CMOS technology feature size worsens the resilience concerns due to factors like aging. This paper addresses the overarching dependability issue of advanced deep neural networks (DNN) accelerators from the aging perspective. Especially, a comprehensive survey and taxonomy of techniques used to evaluate and mitigate aging effects are introduced. We cover different aging effects like permanent faults, timing errors, and lifetime issues. We review research by the layer-wise approach and categorize several resilience classes to bring out major features. The concluding part of this review highlights the questions answered and several future research directions. This study is expected to benefit researchers in different areas of DNN deployment, especially the dependability of this emergent paradigm.